Gaussian Elimination: Solving Systems of Linear Equations

[matqkks]

Is it correct that the Gaussian elimination procedure is used in computer software to solve systems of linear equations?

 

[Petr Mugver]

http://www.mathworks.com/access/helpdesk/help/techdoc/math/f4-983672.html

 

[adriank]

In short: yes (with pivoting for numerical stability), but it's far from the only way, and in certain cases other methods may be better (for example, some method based on conjugate gradients is good when the matrix is sparse, and matrix decomposition is useful for when you want to solve Ax = b for several different b).

 

[hotvette]

There are a variety of matrix decompositions that are used in solving sets of linear equations. LU decomposition is based on Gauss elimination:

http://en.wikipedia.org/wiki/LU_decomposition

but other methods (e.g. Cholesky, LDLT, QR, SVD, etc.) may not.